Problem: Simplify the following expression and state the condition under which the simplification is valid. You can assume that $n \neq 0$. $p = \dfrac{10}{6(2n + 7)} \div \dfrac{n}{4n(2n + 7)} $
Explanation: Dividing by an expression is the same as multiplying by its inverse. $p = \dfrac{10}{6(2n + 7)} \times \dfrac{4n(2n + 7)}{n} $ When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ 10 \times 4n(2n + 7) } { 6(2n + 7) \times n } $ $ p = \dfrac{40n(2n + 7)}{6n(2n + 7)} $ We can cancel the $2n + 7$ so long as $2n + 7 \neq 0$ Therefore $n \neq -\dfrac{7}{2}$ $p = \dfrac{40n \cancel{(2n + 7})}{6n \cancel{(2n + 7)}} = \dfrac{40n}{6n} = \dfrac{20}{3} $